It would be nice to play with the code.
You can see the impact e.g. in the R ecosystem where a good chunk of packages is bio related or the fact that the only user-friendly ontology tool (protege) and the main example of good use of related graph concepts is from bioinformatics
The basic uses of SQL are indeed easy to learn, but quickly you find out that many types of nested queries are no-nos.
Unfortunately, I never used a graph database in a commercial setting, so I don't have much practical experience beyond just toy projects.
Since it seems like you are using this in a commercial setting, did you have any experience with Prolog as a query language?
Cypher is OK, but doesn't really follow any existing paradigms, and LPGs can be a massive footgun without a semantic layer since you can pretty much throw any property on a node type.
Federation over named graphs, or different sources as well.
Writing in Cypher takes a lot of guessing, and there's no real explanation for why sometimes things that seem like they should work -- don't. It feels like a language designed by an amateur, built around a gimmick syntax of (x)-[y]->(z), but as soon as you need something a little more complex, there's nothing.
GP is in a completely different category of things. It has a deep mathematical formalism behind it, a unique and worth of exploring computation model.
Cypher in comparison to GP is like my 3 y.o doodles compared to Rembrandt's doodles. Superficially, both are a bunch of squiggly lines...
From my experience with how Cypher is implemented in Neo4j (admittedly, from a while back), it was a bunch of regular expressions and some hand-tailored string processing.
There's nothing useful (for programmers who want to use Cypher) in the link you provided, just some information about the work group that works on this language. Without much research, I'd imagine that this is an organization sponsored or otherwise supported by Neo4j to promote the use of their database.
Being able to match patterns in a graph is pretty much how you retrieve data. Being able to identify properties of relationships is what Cypher does extremely well.
The GP thing from the OP is mathematical and useless for most software engineers.